2.1.

Cell Preparation

Human mesenchymal stem cells (hMSCs; Lonza) were cultured and maintained in a regular 75T flask (SPL) with Dulbecco’s modified Eagle’s medium (Lonza) supplemented with 10% fetal bovine serum (Gibco) and 1% (v/v) penicillin and streptomycin (Gibco). The cells were stored in an incubator (Panasonic) at 37°C with 5% ${\mathrm{CO}}_2$ and used until eighth passage. Fluorescence imaging of the cell body was performed by labeling the cells using calcein-AM (Thermo Fisher Scientific).

2.2.

Immunofluorescence Staining

Immediately after the acquisition of SHG images, hMSCs were fixed with 4% paraformaldehyde (Biosesang; Korea) for over 1 h. The fixed cells were treated sequentially with 0.4% Triton X-100 (Triton X-100) and with 5% bovine serum albumin (Sigma-Aldrich) before staining. In this study, F-actin and vinculin were stained to explain not only filopodia contraction but also protrusion with deformation of the matrix based on the previous study.³³ The cells were stained with a vinculin antibody (hVIN-1; Sigma-Aldrich) diluted (1:200) within the microchannel device and incubated overnight at room temperature. The treated cells were washed five times using a $1\times$ phosphate buffer solution with a 0.1% Tween-20 (PBST). An Alexa Fluor 568-conjugated antimouse IgG secondary antibody (1:200; Life Technologies), Alexa Fluor 488 phalloidin (1:200; Life Technologies), and Hoechst (33342; 1:3000; Life Technologies) were added and stored in the dark for 2 h. Finally, the stained sample was gently washed five times with PBST, and fluorescent images were obtained using a confocal microscope (LSM 800, Carl Zeiss). We identified colocalized areas of actin and vinculin by performing a Boolean (AND) operation between confocal fluorescent images of proteins, to find the FA sites.

2.3.

Collagen Gel Preparation

Collagen gels were prepared by mixing collagen type I (rat tail tendon, $3.5\mathrm{mg}/\mathrm{mL}$; Corning) with $10\times$ phosphate buffer saline (Gibco), deionized water, and 0.5 N NaOH to achieve a pH of 7.4. Collagen gels were prepared at concentrations of 0.5, 1.5, and $2.5\mathrm{mg}/\mathrm{mL}$ to optimize DVC performance. The collagen gel with $2.5\mathrm{mg}/\mathrm{mL}$ concentration was used for cellular experiments. In addition, hMSCs were mixed with the collagen solution at a concentration of $2\times {10}^4\text{cells}/\mathrm{mL}$ to monitor the internal structural deformation of the collagen caused by cells. The prepolymerized collagen solution, including cells, was introduced into the microchannel device³⁴ and stored in a ${\mathrm{CO}}_2$ incubator for gelation (40 min).

To acquire the image of beads embedded in collagen gel, 2% (volume/volume) fluorescent microbeads ($0.2\mu \mathrm{m}$, yellow-green, 2.5% aqueous suspension; Sigma-Aldrich) were uniformly mixed with the prepolymerized collagen solution.

2.4.

3-D Imaging via Microchannel Device Fabrication

To maintain the quality and quantity of the collagen matrix, we used a microchannel device to load the collagen gel onto the channel and maintain its 3-D shape.³⁴ The device was fabricated using polydimethylsiloxane (PDMS; Sylgard 184 Silicone Elastomer, Dow Corning) on a patterned SU-8 silicon wafer manufactured by MicroChem, based on our own design. The PDMS device was cured at 80°C for 2 h. The microchannel in the device was treated with poly-d-lysine (PDL; Sigma-Aldrich) for over 4 h. The PDL-treated device was washed three times with third-order distilled water and stored overnight.

2.5.

Live Cell SHG Microscopy

A schematic illustration of the SHG microscopy system used in this study is shown in Fig. 1(a). A mode-locked Ti:sapphire laser (Chameleon Ultra II, Coherent) with a central wavelength of 815 nm (temporal $\text{pulse width}=140\mathrm{fs}$) was used as a light source. After adjusting the input polarization and power of the light with a half-wave plate and a polarizing beam splitter, the linear polarized state was adjusted to a circularly polarized state with a quarter-wave plate to generate optical axis-independent SHG over the imaging plane.³¹ A pair of galvanometer mirrors (GM1 and GM2) was used with the image delivery lenses in a $4\text{-}f$ configuration to avoid off-axis scanning distortion. Another $4\text{-}f$ system between GM2 and an objective lens (OBJ; $60\times$, 0.9 NA, Olympus) was adopted as a beam expander, filling the back aperture of the OBJ to attain maximum numerical aperture. Two photomultiplier tubes (PMT; Hamamatsu) were used in a photon-counting mode for signal detection. PMT1 was used to detect the two-photon fluorescence from fluorescent-labeled beads or cells in the backward direction. PMT2 detected the SHG signal in the forward direction using a dichroic mirror (Semrock) in conjunction with a bandpass filter (Semrock) to exclude the excitation light. Axial scanning was performed via computer-controlled translation of the OBJ using an OBJ positioner (MIPOS 500, PiezoJena). Samples were prepared in an on-stage incubator (Live Cell Instruments) at a temperature of 37°C and 5% ${\mathrm{CO}}_2$ concentration with humidity to maintain cell viability for long-term measurements. The microscopic images were captured at a pixel resolution of $512\times 512\times 200\text{voxels}$, and the acquisition time interval was set to 30 min for 3 h.

Fig. 1

SHG microscopy and effect of collagen concentration for validation of the DVC algorithm. (a) Schematic of SHG microscopy. HWP, half-wave plate; QWP, quarter-wave plate; GM1 and GM2, galvanometric mirrors; PMT1 and PMT2, photomultiplier tube; and OBJ, objective lens ($60\times$). (b) Volume image of collagen type I gel at $2.5\mathrm{mg}/\mathrm{mL}$ concentration using SHG microscopy. (c) Stacked SHG image of collagen type I. (d) Measured deformation map after 2.0 voxels ($0.59\mu \mathrm{m}$) of artificial deformation onto the $x$-axis at concentrations of 0.5, 1.5, and $2.5\mathrm{mg}/\mathrm{mL}$. Scale bars: $50\mu \mathrm{m}$ in (b) and (c).

2.6.

Preprocessing and Virtual Deformation of Volumetric Image and DVC Analysis

Using a custom MATLAB™ (2016, MathWorks) script, the stacks of images obtained from each measurement were compared to remove unwanted focus or stage drift. To verify the validity of the DVC analysis with an SHG image, artificial deformation was applied to volumetric images of collagen gel and fluorescent beads obtained in the same laboratory setup. Deformations were applied for each spatial axis and measured via DVC analysis. The fast iterative digital volume correlation (FIDVC) algorithm was applied to measure the complex 3-D displacements.³⁰ FIDVC is an efficient method of DVC used for large nonlinear 3-D transformation fields. Because the reliability of DVC analysis depends on the subset size configuration, the configuration was carefully measured according to the specimen. In this system, a 10-voxel subset spacing and $40\times 40\times 40\text{voxel}$ subset size were used for the FIDVC analysis. To compute the cell-induced deformation, the image stack obtained immediately after the gelation was considered to be the zero-deformation state.

3.1.

Verification of DVC Analysis using Collagen Gel Matrix

We first demonstrated that SHG microscopy could visualize the collagen fiber structure in 3-D with a field of view (FOV) of $150\times 150\times 100\mu \mathrm{m}$, as shown in Fig. 1(b). Naturally, the reconstructed SHG images of collagen gel indicate that a higher concentration of collagen gel yielded a denser and more uniform structure. We tested three different collagen concentrations of 0.5, 1.5, and $2.5\mathrm{mg}/\mathrm{mL}$ as shown in Fig. 1(c) left, middle, and right, respectively. Following measurement of the stack of images from each concentration of collagen gel, uniform translations (2.0 voxels; $0.59\mu \mathrm{m}$) were applied for each stack, and the global deformation was estimated with DVC analysis. Figure 1(d) shows the displacement map for each concentration of the collagen gel. The mean values of deformation were 1.83 ($0.54\mu \mathrm{m}$), 1.92 ($0.57\mu \mathrm{m}$), and 1.96 ($0.58\mu \mathrm{m}$) voxels, and the standard deviations (SD) were 0.22 ($0.07\mu \mathrm{m}$), 0.15 ($0.04\mu \mathrm{m}$), and 0.09 ($0.02\mu \mathrm{m}$) voxels corresponding to 0.5, 1.5, and $2.5\mathrm{mg}/\mathrm{mL}$, respectively. The collagen gels with $2.5\mathrm{mg}/\mathrm{mL}$ concentration show the closest value of deformation to an applied translation of 2.0 voxels ($0.59\mu \mathrm{m}$) and the smallest SD of 0.09 ($0.02\mu \mathrm{m}$). As a result, the collagen gel at $2.5\mathrm{mg}/\mathrm{mL}$ facilitated the detection of deformation reliably with DVC analysis. Although a higher concentration of collagen gel yielded a finer and uniform matrix, a very high concentration of collagen gel tends to prohibit cellular motion.³² Therefore, we used $2.5\mathrm{mg}/\mathrm{mL}$ of collagen concentration in our study.

To verify the accuracy of the collagen gel deformation measurement using SHG microscopy, we compared the displacement based on two different correlation features: the fluorescent images of microbeads, a proven method for DVC analysis,⁹ and SHG images of the collagen fibers. First, the microbead fluorescent images were captured simultaneously with SHG images of the collagen matrix structure. Then, translations were applied to both the microbead-based fluorescence and SHG images using a computer. Translations had magnitudes of 2, 4, and 6 voxels and were in each of the $x$-, $y$- (0.59, 1.18, and $1.77\mu \mathrm{m}$), and $z$ (1.0, 2.0, and $3.0\mu \mathrm{m}$)-directions. DVC was used to compute the displacements by comparing translated image stacks to untranslated ones. For fluorescence and SHG images, the mean errors were 0.08 ($0.024\mu \mathrm{m}$) and 0.03 ($0.008\mu \mathrm{m}$) voxels, taken from the $x$-, $y$-, and $z$-directions. The $z$-axis error was slightly worse than that of the $x$- and $y$-axes, because the sampling resolution of the $x$- and $y$-axes was $0.29\mu \mathrm{m}$, which was better than the $0.5\mu \mathrm{m}$ of the $z$-axis. Nevertheless, the mean errors in using DVC on SHG images are $\sim 10\mathrm{nm}$, which is smaller than the diameter of a collagen fibril (several hundred nanometers).³⁵ These results indicate that errors were negligible and that analysis of SHG images by DVC was reliable.

To compare the accuracy of DVC in the collagen matrix deformation induced by living cells (hMSC), we carried out the experiment using the same method as for the artificial deformation. Figure 2(b) (left) shows the magnitude of the 3-D deformation map using the conventional fluorescent beads method, and Fig. 2(b) (right) shows the map of the collagen gel (imaged with SHG) as a stack of $xy$-slices. The map of collagen deformation showed large displacements around the cells, located at the center of the imaging volume (square with dotted line; approximate cell size $30\mu \mathrm{m}$), indicating cells pushing or pulling on the collagen fibers, as shown in Figs. 2(b) and 3. The measured deformation around the cell is shown as an inset in Fig. 2(c). The line profile of deformation around the dotted squared region for each modality is plotted as red and blue lines in Fig. 2(c). These data were acquired from a single $xy$-slide at a height of $25\mu \mathrm{m}$ from the bottom. The relative error of the measured deformation is calculated by dividing the magnitude of difference in deformation between beads and collagen by the magnitude of bead deformation. In this line profile of error, the mean value was 0.008, and SD was 0.027. The results of the two sets indicate almost identical deformation and appear to adequately describe the 3-D behavior of the cellular interaction with the surrounding physical environment. We repeated this experiment at five distinct times and obtained consistent results. The mean value of root mean square was $0.036\mu \mathrm{m}$, and SD was $0.021\mu \mathrm{m}$ (data not shown).

Fig. 2

Comparison of accuracy between fluorescent-beads- and SHG-collagen-based DVC algorithms. (a) Comparison of DVC results computed by fluorescent-bead images (solid line) and SHG-collagen images (dashed line) for each of the $x$- (red), $y$- (green), and $z$ (blue)-axes. The error, or difference between the applied displacements and the measured displacements, was computed and plotted. (b) Cell-induced displacements measured via imaging of fluorescent beads (left) and collagen fibers (right). (c) Line profile of displacements along rectangular area (dotted line) of a single $xy$-slide ($\text{height}=25\mu \mathrm{m}$) and its relative error.

Fig. 3

Time-lapse video of fluorescent-bead-embedded collagen gel. Bead (red) and collagen gel (green) show displacements over a single $xy$-slide (Video 1, MPEG, 1.04 MB [URL: https://doi.org/10.1117/1.JBO.23.6.065001.1]).

3.2.

Quantifying 3-D Deformation of ECM using DVC Analysis

Measurement of displacements in the collagen gel matrix facilitated the visualization of the 3-D cell–ECM interactions. Live cell images of hMSC within collagen gels were acquired with SHG microscopy and analyzed with DVC to compute the deformation. Five different samples were imaged and quantified for the matrix displacements. A representative case was plotted as a vector cone-plot map with the colors representing the magnitude of displacement, as shown in Fig. 4(a). The direction of the cone plot shows the displacements of the collagen matrix. Figures 4(b) and 4(c) are enlarged images of the orange- and green-dotted boxes in Fig. 4(a), which show displacement vectors surrounding either filopodia or the centroid of the cell body. Figures 4(b) and 4(c) show that the directions of deformation differ with each position of the cell. To investigate the deformations induced by the cell, the deformation of the collagen gel was computed as a function of distance from the cell surface. In addition, to analyze the deformation direction of cell–ECM, the cone-plot vectors of displacement were decomposed into either normal ($N$) or tangential ($T$) with respect to normal of the adjacent cell surface. Figure 4(b), which shows the protruding tip region, represents the magnitude of the deformation according to the distance from the cell surface, as shown in Fig. 4(d). At the collagen gel near the protruding tip of the cell, the magnitude of the $N$ component was distributed more than the magnitude of the $T$ component. Whereas the magnitude of deformation around the centroid of the cell is modest in Fig. 4(c), most deformation arrows show $T$ components, as shown in Fig. 4(e), suggesting that the cell pulls only the ECM around the cell toward the cell body via a protrusion, such as the one shown in Fig. 4(b). Figure 4(f) is a box plot of the mean magnitude near the tip and the body of cell ($n=5$ for each case).

Fig. 4

Visualization of mechanical deformation between cell and ECM. (a) Cone plot of deformation during hMSC protrusion, (b) filopodia, and (c) centroid of cell body shows different aspects of deformation. (d) and (e) Magnitude of displacement as a function of the distance from the surface. The $N$ and $T$ components around the cell correspond to (b) and (c), respectively. (f) The box plot shows the magnitude of $N$ and $T$ near the tip and body of cells ($n=5$). (g) The box plot shows the distance between the local maximum deformation and the cell surface ($n=5$). Scale bars: $50\mu \mathrm{m}$.

Interestingly, as shown in Fig. 4(d), the location of the maximum value of the displacement was not close to the tip of the protrusion, contrary to our expectations. In most cases, the maximum displacement occurred in a few tens of micrometers away from the cell membrane, which was consistent with the scaling laws in response to a nonlinear elastic material that predicts increase in displacement before decay with distance from cell surface.³⁶ Figure 4(g) is a box plot which represents the distance between the local maximum deformation and the cell surface ($n=5$ for each case).

3.3.

Decomposition of Displacement on the Cell Surface

To differentiate the type of mechanical stress applied from the cell surface, we compared the ratio of displacement vector components decomposed into $N$ and $T$ around its normal surface of the cell membrane. The ratio of the magnitudes of the two vector components was computed as

A typical image of a cell migrating is shown in Fig. 5(a), which has been selected from the four samples imaged. The cell migrated toward the lower right (marked as a yellow arrow) with protrusions in the collagen matrix. The deformation was plotted as a cone plot distributed around the cell body (green-dotted box) and at the end of the protrusion (orange-dotted box). As shown in the cone plot near the cell body, the deformation of the ECM occurred mostly in the direction of cell movement. We quantified this deformation by determining the ratio of $N$ to $T$ on the cell surface, shown in blue ($-1$) and red ($+1$) color. As a result, the tangential components were clearly predominant, as shown in Fig. 5(b). On the other hand, the tip of the protrusion region (orange-dotted box) was remarkable, because the cone plot showed that the direction of deformation was distributed in the direction opposite to cell migration in Figs. 5(a) and 5(c). Figure 5(c) shows the ratio between the $N$ and $T$ components of the cell body surface and the projection of the deformation map for each orthogonal axis on the back plane of the imaging volume, which supports the idea that the FA sites form at the protrusion region, resulting in withdrawal of ECM of the collagen fiber toward the center of the cell body via focal points. Figure 5(d) is an enlarged image of the end of the protrusion facing the front of the migrating cell. As expected, the focal point confirms that the $N$ components occur at the end of the cell. In addition, we realized that the $N$ components were also distributed at the opposite sides of the protrusion region indicated by white arrows in Figs. 5(a) and 5(c). In this region, the branch does not grow forward. Instead, this area seems to support the protrusion of the opposite side.

Fig. 5

Mapping over the cell surface by its deformation component with the cone plot of surrounding collagen matrix in 3-D. (a) Deformation around the cell using the cone plot and $N$ and $T$ components on the cell surface. The cell surface was patched with the ratio determined by Eq. (1). Red color denotes the tangential component, and blue represents the normal component. Yellow arrow denotes the direction of the cell migration and white arrow is the branch opposite to the protrusion direction. (b) Cropped FOV shows tangential deformations mostly occurring at the centroid of the migrating cell body. (c) In the protruding filopodia, normal components are located at the very tip, shown in blue color. Scale bar: $50\mu \mathrm{m}$ in (a), $10\mu \mathrm{m}$ in (b) and (c).

3.4.

Identifying the Focal Adhesion Site Using Time-Lapse Imaging

To investigate the relationship between deformation of the ECM and dynamics of the FAs, we performed time-lapse imaging at time intervals of 30 min for 3 h for four samples. Time-lapse imaging of cell migration during protrusion and retraction shows the step-by-step mechanical interaction between the cell and the surrounding ECM. A typical cone plot is shown in Fig. 6, where the cell shows the typical amoeboid shape and has branch-like protrusion regions within the FA site. In Fig. 6(a), the cell body has limited movement; however, the cell stretches protrusions toward the right over time. Also, deformation of the ECM at the tip of filopodia consistently occurred on the right side of the filopodia tip. The maximum deformation point of the ECM was located at the tip of the filopodia, as shown in Figs. 6(a) and 7. Immediately after time-lapse imaging, we detected the presence of FA by observing the distribution of actin and vinculin using the immunofluorescence assay from the four samples.³³ Vinculin, actin, and the nucleus are represented in red, green, and blue, respectively, as shown in Figs. 6(b) and 6(d). Thus, we confirmed the colocalization of actin and vinculin, regarded as FA, at the tip of the cell (in yellow color) with the deformation occurring consistently as shown in the green-dotted box in Fig. 6(b). However, the orange-dotted boxes also showed a strong colocalization of actin and vinculin in Fig. 6(b), without a strong deformation of ECM. Although these protrusion branches connected to the ECM through an FA site, they did not deform the ECM during the experiment. We confirmed this result as shown in the 3-D images in Figs. 6(c) and 6(d). In other words, the cells exerted sustained traction at the FA site in addition to extending their filopodia into the 3-D matrix.

Fig. 6

Time-lapse observation of deformation in the hMSC. (a) Time series of protrusion show maximum strain area following the tip of protrusion. (b) Immunofluorescence image of hMSC immediately after time-lapse imaging. Green- and orange-squared regions show colocalization of vinculin and actin. Cell in the yellow-colored region denotes a colocalized area (blue: nucleus, green: actin, and red: vinculin. Scale bar: $20\mu \mathrm{m}$, 30 min per frame). (c) and (d) represent bird’s-eye views of (a) and (b).

Fig. 7

Cone plot of deformation map based on time-lapse observations of hMSC in 3-D. Scale bar: $20\mu \mathrm{m}$ (Video 2, MPEG, 0.82 MB [URL: https://doi.org/10.1117/1.JBO.23.6.065001.2]).